Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs

S. C. Fang and H. S. J. Tsao
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S. C. Fang: North Carolina State University
H. S. J. Tsao: University of California

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 1, No 5, 73-85

Abstract: Abstract A dual l p-norm perturbation approach is introduced for solving convex quadratic programming problems. The feasible region of the Lagrangian dual program is approximated by a proper subset that is defined by a single smooth convex constraint involving the l p-norm of a vector measure of constraint violation. It is shown that the perturbed dual program becomes the dual program as p→∞ and, under some standard conditions, the optimal solution of the perturbed dual program converges to a dual optimal solution. A closed-form formula that converts an optimal solution of the perturbed dual program into a feasible solution of the primal convex quadratic program is also provided. Such primal feasible solutions converge to an optimal primal solution as p→∞. The proposed approach generalizes the previously proposed primal perturbation approach with an entropic barrier function. Its theory specializes easily for linear programming.

Keywords: Convex quadratic programming; duality theory; perturbation methods (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022655502360

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